A cylindrical pillar is $50 \mathrm{~cm}$ in diameter and $3.5 \mathrm{~m}$ in height.

Question. A cylindrical pillar is $50 \mathrm{~cm}$ in diameter and $3.5 \mathrm{~m}$ in height. Find the cost of painting the curved surface of the pillar at the rate of Rs. $12.50$ per $\mathrm{m}^{2} .\left[\right.$ Assume $\left.\pi=\frac{22}{7}\right]$


Solution:

Height $(h)$ cylindrical pillar $=3.5 \mathrm{~m}$

Radius $(r)$ of the circular end of pillar $=\frac{50}{2}=25 \mathrm{~cm}$

$=0.25 \mathrm{~m}$

CSA of pillar $=2 \pi r h$

$=\left(2 \times \frac{22}{7} \times 0.25 \times 3.5\right) \mathrm{m}^{2}$

$=(44 \times 0.125) \mathrm{m}^{2}$

$=5.5 \mathrm{~m}^{2}$

Cost of painting $1 \mathrm{~m}^{2}$ area = Rs $12.50$

Cost of painting $5.5 \mathrm{~m}^{2}$ area $=$ Rs $(5.5 \times 12.50)$

$=$ Rs $68.75$

Therefore, the cost of painting the CSA of the pillar is Rs $68.75$.

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